[PDF] Module 6 – Lexical Phase - RE to DFA

View - Download Module 6 – Lexical Phase - RE to DFA

Previous PDF

Next PDF

Module 6

T s 6.1

· Thompsons subset construction algorithm

· Syntax tree

6.2 Syntax Tree Procedure

The following algorithm,

SyntaxTree

Input: Regular Expression

1. Augment the regular expression r #which is used as an end marker

r #

2. Construct a syntax tree for r#

Traverse the tree to construct functions nullable, firstpos, lastpos, and followpos firstpos, lastpos, and followpos

6.2.1 Syntax Tree construction

Based on the precedence of the regular expression operators*, + and . a syntax tree is . and this will + and this will also have two # will be the leaf nodes of this expression. a and b are input+ operator then the

Using this method and the precedence of operators

6.2.2. Nullable( )

After constructing the syntax tree, for every symbol in the syntax tree, the function nullable() is . Hence, if a leaf node is labeled with then the nullable information a a of that node is set to True and for all other input alphabet a such that a is not an operator,

Fa. For the regular expression operators,

and operation while the union operator is considered as or operation for + and . or and and indicates the logical operators. Hence, nullable(+) will be set True if any of its children is nullable and nullable(.) will be set to True only if both of its True

6.2.3 firstpos()

The n. a, the firstpos(a) is the integer assigned to it , firstpos( ) is defined as empty. After assigning the firstpos( ) + .with children c1 and c2, else

6.2.4 last

lastpos( n. a, the lastpos(a) is also the integ , lastpos( ) is defined as empty, since + and . and with children c1 and c2, Table 6.1 Summary of the functions nullable(), firstpos() and lastpos() n nullable(n)firstpos(n)lastpos(n)

Leaf e AE AE

Leaf c c nullable(c1) true

6.2.5 followpos(n)

followpos( i

1. for n do

n c 1 c 2 then i in lastpos(c 1 do followpos(i) := followpos(i) È firstpos(c 2 end do n i in lastpos(n) do followpos(i) := followpos(i) È firstpos(n) end do

Algorithm 6.1: Followpos() construction

based on the Kleene closure operator.

6.2.6 DFA

The construction algorithm is given in Algorithm 6.2. Initially, the firstpos s

Dstates

while do mark each input symbol Î S do let a. a if Uthen add Dtran

Algorithm 6.2

Example 6.1 : Construct a minimized DFA for the regular expression (a|b)*abb

In example 6.1,

c), the syntax tree is constructed and is shown in False. Similarly, other interior concatenation nodes will also have

False.

Figure 6.3 Syntax tree wit.

and lastpos() and is ind1

2. The firstpos( | ) and the laspos( | ) is given by the union of the firstpos and lastpos of its

., which is a pa (3),

Followpos(n)

1 s firstpos() as the s firstpos() is {1,2,3} and hence, this set is the start state. In this set, 1 and 3 a. Hence, to define the edge from this state on a, we need to a. Similarly, the state 2 corresponds to input b. Hence, followpos(2) is to be considered for the edge on b from {1,2,3} which is the same

1 and 3 corresponds to a

a. For b, nodes 2, 4

6. In the state6 is contained in the set representing {1,2,3,6}

s construction algorithm.

Summary

In this module, we discussed the construction of minimized DFA which is performed from thequotesdbs_dbs14.pdfusesText_20

[PDF] (a+b)* regular expression examples

[PDF] (a+b)* regular expression language

[PDF] (yn) diverges

[PDF] .jinit r

[PDF] .net application performance testing tools

[PDF] .net core load testing tools

[PDF] .net gui automation testing tools

[PDF] .net web application load testing tools

[PDF] .net xml localization

[PDF] 0.45 sodium chloride (1/2 normal saline)

[PDF] 00000 zip code usa

[PDF] 0016h is an example of ....addressing mode

[PDF] 0417/11/m/j/16 ms

[PDF] 0417/12/m/j/14 ms

[PDF] 0417/13/m/j/15 ms